Generalized extended Lagrangian Born-Oppenheimer molecular dynamics

Abstract

Extended Lagrangian Born-Oppenheimer molecular dynamics based on Kohn-Sham density functional theory is generalized in the limit of vanishing self-consistent field optimization prior to the force evaluations. The equations of motion are derived directly from the extended Lagrangian under the condition of an adiabatic separation between the nuclear and the electronic degrees of freedom. We show how this separation is automatically fulfilled and system independent. The generalized equations of motion require only one diagonalization per time step and are applicable to a broader range of materials with improved accuracy and stability compared to previous formulations.

Graph-based linear scaling electronic structure theory

“…Without the adaptivity of the graph-based method, the divide and conquer approach needs a large cutoff radius, R cut , to reach sufficient convergence in the calculation of the density matrix for the water system, which leads to a significant overhead. With the graph-based framework as demonstrated here in combination with a modern formulation of Born-Oppenheimer molecular dynamics, [42][43][44][45][46][47][48][49][50] these problems can be avoided.…”

“…Figure 5 shows the fluctuations of the total energy during a microcanonical molecular dynamics simulation of liquid water that was performed using LATTE 58 and the extended Lagrangian formulation of Born-Oppenheimer molecular dynamics. 50,[67][68][69][70] The density matrix was calculated from a partitioning over separate subgraphs of S τ (t), with one water molecule per core. For the Fermi-operator expansion (at zero temperature) we used the recursive SP2 algorithm.…”

“…The graph-based electronic structure theory combines the natural parallelism of a divide and conquer approach [12][13][14][15][16][17] with the automatically adaptive and tunable accuracy of a thresholded sparse matrix algebra, [18][19][20][21][22][23][24][25][26][27][28][29][30][31] which can be combined with fast, low pre-factor, recursive Fermi operator expansion methods [32][33][34][35][36][37][38][39][40][41] and can be applied to modern formulations of Born-Oppenheimer molecular dynamics. [42][43][44][45][46][47][48][49][50] The article is outlined as follows: first we introduce the graph-based formalism for general sparse matrix polynomials expanded over separate subgraphs, thereafter we apply the methodology to the Fermi-operator expansion in electronic structure theory with demonstrations for a protein-like structure of polyalanine solvated in water, before analyzing applications in molecular dynamics simulations. At the end we give our conclusions.…”

Scalable Reactive Molecular Dynamics Simulations for Computational Synthesis

“…(7) and (8) , is 2 [15]. We have found that the same value works for XRMD as well, and K = 2.0 will be use in the numerical tests discussed below.…”

“…(1) causes serious energy drift. Niklasson proposed an extended Lagrangian scheme [14,15] that achieves excellent long-time energy conservation with drastically reduced number of iterations. In fact, an extended Lagrangian scheme with no iteration (i.e., requiring only one evaluation of energy gradient per MD time step) has recently been demonstrated [16].…”